Rational designs

Cui, Zhen; Xia, Jiacheng; Xiang, Ziqing

doi:10.1016/j.aim.2019.06.012

Cited by 5 publications

(1 citation statement)

References 22 publications

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“…Since then, more concise proofs and explicit constructions have been under intense investigation in combinatorial mathematics (see e.g., Refs. [68][69][70][71][72] and the references therein). In particular, it was only recently that constructions in general cases [73] and explicit constructions, in the sense that the algorithm for the construction is given in a computable form [74], were proposed.…”

Section: Introductionmentioning

confidence: 99%

Quantum circuits for exact unitary $t$-designs and applications to higher-order randomized benchmarking

Nakata,

Zhao,

Okuda

et al. 2021

Preprint

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A unitary t-design is a powerful tool in quantum information science and fundamental physics. Despite its usefulness, only approximate implementations were known for general t. In this paper, we provide for the first time quantum circuits that generate exact unitary t-designs for any t on an arbitrary number of qubits. Our construction is inductive and is of practical use in small systems. We then introduce a t-th order generalization of randomized benchmarking (t-RB) as an application of exact 2t-designs. We particularly study the 2-RB in detail and show that it reveals the selfadjointness of quantum noise, a new metric related to the feasibility of quantum error correction (QEC). We numerically demonstrate that the 2-RB in one-and two-qubit systems is feasible, and experimentally characterize the background noise of a superconducting qubit by the 2-RB. It is shown from the experiment that the interactions with adjacent qubits induce the noise that may result in an obstacle toward the realization of QEC.

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